X^(-4/3)-2x^(2/3)-8=0

[latex]x^{-\frac43}-2x^{-\frac23}-8=0\\x^{-\frac23}=t,\;x^{-\frac43}=t^2,\;t\ \textgreater \ 0\\t^2-2t-8=0\\D=4+4\cdot8=36\\t_{1,2}=\frac{2\pm6}2\\t_1=4\\t_2=-2\ \textless \ 0\;-\;He\;nogx.\\x^{-\frac23}=4\\\frac1{\sqrt[3]{x^2}}=4\\\sqrt[3]{x^2}=\frac14\\x^2=\frac1{64}\\x=\pm\frac18.[/latex]